Related papers: On the Hessian-cscK equations
We study the quantization of coupled K\"ahler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics''. We prove the existence and weak convergence of balanced…
We develop a variational calculus for a certain free energy functional on the space of all probability measures on a Kahler manifold X. This functional can be seen as a generalization of Mabuchi's K-energy functional and its twisted…
The Donaldson-Fujiki K\"ahler reduction of the space of compatible almost complex structures, leading to the interpretation of the scalar curvature of K\"ahler metrics as a moment map, can be lifted canonically to a hyperk\"ahler reduction.…
We consider a complexification of the Euler equations introduced by \v{S}ver\'ak which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analytic regularity and, moreover, we exhibit solutions…
In this work we construct several black hole metrics which are consistent with the generalized uncertainty principle logarithmic correction to the Bekenstein-Hawking entropy formula. After preserving the event horizon at the usual position,…
We establish energy-balance for weak solutions of the stochastically forced incompressible Euler equations, enjoying H\"older regularity $C^{\alpha}$, $\alpha>1/3$. It is well known as the Onsager's conjecture for the deterministic…
In every point of a K\"ahler manifold there exist special holomorphic coordinates well adapted to the underlying geometry. Comparing these K\"ahler normal coordinates with the Riemannian normal coordinates defined via the exponential map we…
The K\"ahler metric which has been constructed by present author is used in this paper to find an exact solution of Einstein equations with energy-momentum tensor of special type. The type of $T_{ij}$ admits in particular to use it as…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
We construct a family of quasimetric spaces in generalized potential theory containing $m$-subharmonic functions with finite $(p,m)$-energy. These quasimetric spaces will be viewed both in $\mathbb{C}^n$ and in compact K\"ahler manifolds,…
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and P\"oschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
We show that the Mabuchi energy of any polarized manifold (X,L) is (bounded below) proper on the full space of Kahler metrics in the first Chern class of L if and only if (X,L) is asymptotically (semi)stable. In particular it now follows…
Let (X,L) be a polarized K\"ahler manifold that admits an extremal K\"ahler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is…
We solve the geodesic equation in the space of K\"ahler metrics under the setting of asymptotically locally Euclidean (ALE) K\"ahler manifolds and we prove global $\mathcal{C}^{1,1}$ regularity of the solution. Then, we relate the solution…
We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or H\"older continuous for any exponent $\theta<\frac{1}{16}$. Using the techniques introduced in \cite{DS12}…
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the P\"oschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this…
We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…